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A five-digits number is formed by using the digits $1,2,3,4,5$ with no repetition. The probability that the numbers 1 and 5 are always together, is
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The correct answer is:
$\frac{2}{5}$
The total number of possible five-digit numbers $=5$ !
The total number of possible five-digit numbers in which 1 and 5 are always together $=2 \times 4$ !
$\therefore$ Required probability $=\frac{2 \times 4 !}{5 !}=\frac{2 \times 4 !}{5 \times 4 !}=\frac{2}{5}$
The total number of possible five-digit numbers in which 1 and 5 are always together $=2 \times 4$ !
$\therefore$ Required probability $=\frac{2 \times 4 !}{5 !}=\frac{2 \times 4 !}{5 \times 4 !}=\frac{2}{5}$
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